Question

use rigid motions to write a proof of the converse of the isosceles triangle theorem. given: $\angle j\cong\angle l$ prove: $\overline{jk}\cong\overline{kl}$ reflect $\triangle jkl$ horizontally right across a line perpendicular to $\overline{jl}$ to form image $\triangle lkj$. this shows that

Explanation:

Step1: Property of reflection

A reflection is a rigid motion. Rigid motions preserve side - lengths and angles. When we reflect \(\triangle JKL\) across a line perpendicular to \(\overline{JL}\) to get \(\triangle L'K'J'\), we know that \(\overline{KL}\) and \(\overline{K'J'}\) are corresponding sides.
Since reflection is a rigid motion, corresponding sides of the pre - image (\(\triangle JKL\)) and the image (\(\triangle L'K'J'\)) are congruent.

Answer:

\(\overline{KL}\cong\overline{K'J'}\)